Most people are familiar with angles measured in degrees. A full circle measures 360?. Parts of a degree are often measured two different ways, degrees decimal and DMS (degree, minute, second).

We can always show a degree as we would any decimal number by showing its whole units followed by its fractional portion. For example, 75.23? means that we have 75 degrees and twenty-three hundredths of a degree.

In the DMS system, each degree is made up of 60 minutes (or arcminutes) and is marked with a ` . Each minute is made up of 60 seconds (or arcseconds) and is marked with a . This is read as 36 degrees, 14 minutes, 52 seconds.

Radians are more common in computer programming and mathematics. To understand radians, you must understand the constant Pi (often given the symbol of the lowercase Greek letter pi). Pi is an irrational and transcendental number (its decimal notation never ends) and is the circumference of any circle divided by that circle's diameter. An approximate value (to 20 decimal places) is Pi = 3.1415926535897932385. The value of Pi can also be found using this code.

Pi = 4 * Atn(1)

With the radian system, a full circle has 2*Pi (6.2831853071795864770) radians. Unlike degrees, radians are not marked with any form of a symbol. FreeBASIC, like most programming languages, accepts angle measurements in radians and not degrees.

To convert between radians and degrees (decimal) you can use the following code.